This looks a lot like the issue I had with during development IE8, for which I made a code exception (disabled some javascript functions for IE8). Sometimes if there are javascript errors, execution of any javascript will be disabled, which prevents the shoutbox from functioning. I have no IE9 here, so maybe you can see if you get javascript errors when you load the shoutbox. If there are errors, can you post them here?

It took a while, but i found out that Microsoft offers free virtual machines with all major IE versions. I downloaded the one for IE9, and found that it does load your shoutbox without any errors. See the attached screenshot. Maybe you have some Internet Explorer settings disabled or restricted, like javascript.

If it also happens with newer IE versions, then it can't really be anything other than some configuration issue. If you have a computer capable of running virtual machines, you could download the one with IE9 from the following location, and compare the settings: